Questions in Section Calculus II

What is the least number of subdivisions that will guarantee, with the standard error bounds, that the result is accurate upto 4 decimal places? Consider using midpoint method to estimate the integral `int_0^0.5e^(-x^2)dx`.

The demand function for a certain product is given by `p=-0.01x^2-0.2x+10`, where `p` represents the unit price in dollars and `x` is the quantity demanded measured in units of a thousand. Determine the consumer surplus if the price is set at $2.